Computational Methods and Function Theory 1 (2001), No. 1, 289--299
Copyright Heldermann Verlag 2001
Mingliang L. Fang
mlfang@pine.njnu.edu.cn, Department of Mathematics, Nanjing Normal University, Nanjing 210097, P. R. China.
Lawrence Zalcman
zalcman@macs.biu.ac.il, Department of Mathematics and Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel.
This paper continues our investigation of conditions involving values shared by combinations of a function and its derivatives which imply the normality of families of meromorphic functions. In particular, we prove that if $\mathcal{F}$ is a family of meromorphic functions on the plane domain $D$ all of whose zeros have multiplicity at least $k\ge 1$, and if $f(z)f^{(k)}(z)=a\Leftrightarrow f^{(k)}(z)=b$ for all $f\in\mathcal{F}$ and $z\in D$ (where $a\ne0$ and $b$ are fixed complex numbers), then~$\mathcal{F}$ is normal on $D$.
Keywords: Normal families, shared values.
MSC 2000: 30D45.
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